https://file.aiquickdraw.com/mathbot/file/1725835297688twqicgm6.jpg

Let's solve the problem from the image you provided. The question asks to evaluate \((f + g)(x)\) if \(f(x) = 2x^2\) and \(g(x) = 3x - 2\) when \(x = 3\).

**Step-by-Step Solution:**

1. **Calculate \(f(3)\):**
   \[
   f(x) = 2x^2 \implies f(3) = 2(3)^2 = 2 \times 9 = 18
   \]

2. **Calculate \(g(3)\):**
   \[
   g(x) = 3x - 2 \implies g(3) = 3(3) - 2 = 9 - 2 = 7
   \]

3. **Calculate \((f + g)(3)\):**
   \[
   (f + g)(x) = f(x) + g(x) \implies (f + g)(3) = f(3) + g(3) = 18 + 7 = 25
   \]

Therefore, the correct answer is **25**.

Would you like more details or have any questions?

Here are some related questions to consider:

1. How do you find the value of a function at a specific point?
2. What are some other ways to combine functions, such as multiplication or division?
3. How do you evaluate the sum of two functions at different points?
4. What is the impact of different operations on the graphs of combined functions?
5. How do you interpret function notation and apply it in various contexts?

**Tip:** Always substitute the value of \(x\) correctly when evaluating functions to avoid errors.

Evaluate (f + g)(x) if f(x) = 2x^2 and g(x) = 3x - 2 when x = 3.

Learn how to evaluate the sum of functions at a specific point, using a quadratic function f(x) = 2x^2 and a linear function g(x) = 3x - 2. This step-by-step guide shows how to solve for (f + g)(x) when x = 3. Suitable for students in Grades 9-10.

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